সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=33$$ এবং সাধারণ অনুপাত: $$r=0.5454545454545454$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=33$$

$$a_2=a_1·r^{n-1}=33\cdot {0.5454545454545454}^{2-1}=33\cdot {0.5454545454545454}^1=33\cdot 0.5454545454545454=18$$

$$a_3=a_1·r^{n-1}=33\cdot {0.5454545454545454}^{3-1}=33\cdot {0.5454545454545454}^2=33\cdot 0.29752066115702475=9.818181818181817$$

$$a_4=a_1·r^{n-1}=33\cdot {0.5454545454545454}^{4-1}=33\cdot {0.5454545454545454}^3=33\cdot 0.16228399699474075=5.355371900826444$$

$$a_5=a_1·r^{n-1}=33\cdot {0.5454545454545454}^{5-1}=33\cdot {0.5454545454545454}^4=33\cdot 0.08851854381531314=2.921111945905334$$

$$a_6=a_1·r^{n-1}=33\cdot {0.5454545454545454}^{6-1}=33\cdot {0.5454545454545454}^5=33\cdot 0.048282842081079885=1.5933337886756362$$

$$a_7=a_1·r^{n-1}=33\cdot {0.5454545454545454}^{7-1}=33\cdot {0.5454545454545454}^6=33\cdot 0.026336095680589026=0.8690911574594379$$

$$a_8=a_1·r^{n-1}=33\cdot {0.5454545454545454}^{8-1}=33\cdot {0.5454545454545454}^7=33\cdot 0.014365143098503105=0.4740497222506025$$

$$a_9=a_1·r^{n-1}=33\cdot {0.5454545454545454}^{9-1}=33\cdot {0.5454545454545454}^8=33\cdot 0.007835532599183511=0.25857257577305587$$

$$a_{10}=a_1·r^{n-1}=33\cdot {0.5454545454545454}^{10-1}=33\cdot {0.5454545454545454}^9=33\cdot 0.004273926872281915=0.1410395867853032$$